(1) Field of Invention
The present invention relates to a system for catastrophe prediction and, more particularly, to a system for catastrophe prediction via estimated network autocorrelation.
(2) Description of Related Art
The dynamics of complex systems as they approach a tipping point is an important area of study, as gradual, hard to detect changes in equilibria may suddenly induce catastrophic systemic shifts such as economic collapses, epileptic shocks, and climate changes. Warning signals for when these transitions become imminent are therefore extremely desirable.
Very little work has been done toward making predictions of critical transitions. In the most notable reference by Scheffer et al. (see the List of Cited Literature References, see Literature Reference No. 16), two forms of early warning signals (EWSs) were proposed: increased temporal correlation and increased spatial correlations of the system states. Dakos et al. (see Literature Reference No. 5) primarily focused on the increased spatial correlation as a better leading indicator of approaching critical transitions. Furthermore, Guttal et al. (see Literature Reference No. 10) proposed the skewness of the spatial statistics of the system behavior as another viable EWS.
Gradual, hard to detect changes in equilibria may suddenly induce catastrophic systemic shifts such as economic collapse (see Literature Reference No. 11), epileptic shock (see Literature Reference No. 13), and climate change (see Literature Reference No. 6). Warning signals for when these transitions become imminent are, therefore, extremely desirable. Observation of the phenomenon known as critical slowing down has recently successfully served as a warning signal in many bifurcating ecological systems (see Literature Reference No. 17). A system destabilizing through critical slow down exhibits a decreased recovery rate from small perturbations, a property quantifiable through increased time autocorrelation (see Literature Reference No. 16), spatial autocorrelation (see Literature Reference No. 19), and emergence of self-organizing patterns (see Literature Reference No. 5).
The early warning signal (EWS) of critical slowing down was proposed by Scheffer et al. (see Literature Reference No. 16) for simple one-node and two-node systems. Dakos et al. (see Literature Reference No. 5) further verified that spatial correlations increase for a 2500-node (50×50 spatial grid) coupled dynamical system. They compared the merits of temporal and spatial indicators under different system configurations and also verified that the spatial correlations of a strongly connected system increase more rapidly than a weakly connected system. Further, Guttal et al, (see Literature Reference No. 10) proposed the utility of changes in spatial skewness as another indicator of impending regime shifts, as well as the increased spatial correlations. However, these prior studies provide a basis for making predictions of approaching transition only in a qualitative manner (e.g., “a transition is coming”); they do not offer measures to make any quantitative predictions (e.g., “how soon will the transition happen?”). Additionally, these studies do not generalize to arbitrary interaction strengths between system nodes, because they model spatially arranged living systems whose interactions depend only on physical distances.
The studies above never take into account the non-homogeneous system connectivity structure observed in real world systems as a crucial factor in the process of analyzing the EWSs. The studies above either consider simple one-node or two-node systems, or multi-node spatial systems having homogeneous topographic connectivity between neighboring spatial nodes. Each of the aforementioned methods exhibit limitations that make them incomplete. Thus, a continuing need exists for a method with the capability to analyze wide ranges of complex systems that have varied degrees of interactions between system elements.